A fourth view is the transformation of emotion, as in Housman's fine phrase on the arts: they `` transform and beautify our inner nature ''.

Clearly, the transformation is involutorial.

Moreover, from the definitive transformation of intercepts on the generators of Af, it is clear that the only points of Q at which a line can meet its image are the points of Aj.

Now consider the transformation of the lines of a bundle with vertex, P, on **zg which is effected by the involution as a whole.

the way in which the transformation of state depends on the operating variables for the main types of reactors is discussed in the next chapter.

He recognized that whatever transformation may be effected in the first stage of an R-stage process, the remaining stages must use an optimal Af-stage policy with respect to the state resulting from the first stage, if there is to be any chance of optimizing the complete process.

The whole role, by the way, is a considerable transformation for anyone who has seen Seigner in his other parts.

According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.

To avoid attacks based on simple algebraic properties, the S-box is constructed by combining the inverse function with an invertible affine transformation.

Bruce Hindmarsh suggests that the secular popularity of " Amazing Grace " is due to the absence of any mention of God in the lyrics until the fourth verse ( by Excell's version, the fourth verse begins " When we've been there ten thousand years "), and that the song represents the ability of humanity to transform itself instead of a transformation taking place at the hands of God.

James Basker also acknowledged this force when he explained why he chose " Amazing Grace " to represent a collection of anti-slavery poetry: " there is a transformative power that is applicable ...: the transformation of sin and sorrow into grace, of suffering into beauty, of alienation into empathy and connection, of the unspeakable into imaginative literature.

A transformation of a thermodynamic system can be considered adiabatic when it is quick enough that no significant heat is transferred between the system and the outside.

At the opposite extreme, a transformation of a thermodynamic system can be considered isothermal if it is slow enough so that the system's temperature remains constant by heat exchange with the outside.

The shift in Aalto's design approach from classicism to modernism is epitomised by the Viipuri Library ( 1927 – 35 ), which went through a transformation from an originally classical competition entry proposal to the completed high-modernist building.

Some theories connect these flows directly, implying that there is significant upwelling of dense deep waters within the Southern Ocean, transformation of these waters into light surface waters, and a transformation of waters in the opposite direction to the north.

This is because such flows can produce a net southward flow in the troughs and a net northward flow over the ridges without requiring any transformation of density.

Skewing is an example of a transformation not usually considered.

This gradual transformation is an important consideration when studying the properties of elemental berkelium and its chemical compounds, since the formation of californium brings not only chemical contamination, but also self-radiation damage, and self-heating from the emitted alpha particles.

In linear algebra, a bilinear transformation is a binary function where the sets X, Y, and Z are all vector spaces and the derived functions f < sup > x </ sup > and f < sub > y </ sub > are all linear transformations.

The category of sets is closed monoidal, but so is the category of vector spaces, giving the notion of bilinear transformation above.

Conversely, any affine linear transformation extends uniquely to a projective linear transformations, so the affine group is a subgroup of the projective group.

Specifying the transformation law of Γ is not sufficient to determine Γ uniquely.

: Any linear transformation f: V → A from V to an algebra A over K can be uniquely extended to an algebra homomorphism from T ( V ) to A as indicated by the following commutative diagram:

Every bounded linear transformation from a normed vector space to a complete, normed vector space can be uniquely extended to a bounded linear transformation from the completion of to.

Therefore an even dimensional manifold always admits a ( 1, 1 ) rank tensor pointwise ( which is just a linear transformation on each tangent space ) such that J < sub > p </ sub >< sup > 2 </ sup > = − 1 at each point p. Only when this local tensor can be patched together to be defined globally does the pointwise linear complex structure yield an almost complex structure, which is then uniquely determined.

The transformation mapping p to η can be uniquely inverted ; for example, the x-component of the momentum equals

By the end of her career, Perry ’ s work had undergone a complete transformation and expanded to include not only formal portraits, but also portraits rendered in the Impressionist style and landscapes that were uniquely inspired by her time with Monet at Giverny.

In studying such transformations it is always necessary to distinguish between the material transformation of the economic conditions of production, which can be determined with the precision of natural science, and the legal, political, religious, artistic or philosophic — in short, ideological forms in which men become conscious of this conflict and fight it out.

The " basis " for the tensor field is determined by the coordinates of the underlying space, and the defining transformation law is expressed in terms of partial derivatives of the coordinate functions,, defining a coordinate transformation,

This diagram shows that the natural transformation Φ is completely determined by since for each morphism f: A → X one has

Supposing we exclude the degenerate case where ABCD has zero area, there is a unique such affine transformation T. Drawing out a whole grid of parallelograms based on ABCD, the image T ( P ) of any point P is determined by noting that T ( A ) = A ′, T applied to the line segment AB is A ′ B ′, T applied to the line segment AC is A ′ C ′, and T respects scalar multiples of vectors based at A.

Furthermore, tyrosine kinase activity has been determined to be correlated to cellular transformation.

Knowing the correspondence between a number of points in images, a transformation is then determined to map the target image to the reference images, thereby establishing point-by-point correspondence between the reference and target images.

In mathematics, a homothety ( or homothecy, or homogeneous dilation ) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sends

The ratio of opportunity costs is determined by the marginal rate of transformation.

Mayer not only performed this demonstration, but determined also the quantitative factor of the transformation, calculating the mechanical equivalent of heat.

Its organisation and authority, however, had been determined earlier in the framework of the trilateral political roundtable negotiations preparing the democratic transformation of the political system.

Rodney had determined that the only path to true human development and liberation for the majority of the people of his country was through the transformation of their own lives in a struggle to replace and reshape the neo-colonialist government that dominated their society and prescribed their existence.

* Secondary yolk sac: this first transformation is determined by the modification of its cover, in the connection zone between the epiblast and the Heuser membrane.

This is because " the relationship between actual culture ... on the one hand, and economically determined factors such as class position, on the other, is always problematical, incomplete, and the object of ideological work and struggle .... Cultural relationships and cultural change are thus not predetermined ; rather they are the product of negotiation, imposition, resistance, transformation, and so on .... Thus particular cultural forms and practices cannot be attached mechanically or even paradigmatically to particular classes ; nor, even, can particular interpretations, valuations, and uses of a single form or practice.

The concentration of pollutants in the atmosphere is determined by their transport, or mean velocity of movement through the atmosphere, their diffusion, chemical transformation, and ground deposition.

Specifically, invariance ( or more appropriately covariance ) to local geometric transformations, such as rotations or local affine transformations, can be obtained by considering differential invariants under the appropriate class of transformations or alternatively by normalizing the Gaussian derivative operators to a locally determined coordinate frame determined from e. g. a preferred orientation in the image domain or by applying a preferred local affine transformation to a local image patch ( see the article on affine shape adaptation for further details ).

In studying such transformations it is always necessary to distinguish between the material transformation of the economic conditions of production, which can be determined with the precision of natural science, and the legal, political, religious, artistic or philosophic – in short, ideological forms in which men become conscious of this conflict and fight it out.

Post-perovskite also holds great promise for mapping experimentally determined information regarding the temperatures and pressures of its transformation into direct information regarding temperature variations in the D " layer once the seismic discontinuities attributed to this transformation have been sufficiently mapped out.

The concentration of pollutants in the atmosphere is determined by transport, diffusion, chemical transformation, and ground deposition.